Finite-time stabilization of fractional-order neural networks with time-varying delays: A generalized inequality approach and controller design

This paper explores finite-time stabilization methods for a specific class of neural networks with fractional-order dynamics and time-varying delays. The first contribution involves introducing a generalized inequality, an extension of the existing one, to analyze the finite-time stabilization behavior of the addressed model. This extension has successfully addressed numerous limitations and challenges present in existing works. Additionally, an explicit formula for calculating the finite-time stabilization duration is provided. Subsequently, two types of controllers—delay-independent and delay-dependent feedback controllers—are developed to achieve finite-time stabilization for the neural networks under consideration. The conditions for stability, dependent on both the delay and the order, are formulated as linear matrix inequalities using inequality techniques, Lyapunov stability theory, and the newly proposed finite-time stability inequality. These conditions ensure that the fractional-order neural network model is stabilized in finite-time. The efficacy of the suggested design approach is demonstrated through two numerical case studies.